Nearly Optimal Perimeter Tracking Control for Two Urban Regions With Unknown Dynamics

Perimeter control based on macroscopic fundamental diagrams (MFDs) aims to manipulate the bi-directional transfer flows by adjusting traffic signals on the regional boundary. In this letter, a traffic network consisting of two homogeneous regions with unknown MFD information and constrained inputs is considered, and a data-driven method is proposed for the optimal perimeter tracking control that regulates the number of vehicles in each region to track the desired trajectory dynamics. By transforming the two-region MFD dynamics into an affine nonlinear system with unknown nonlinear dynamics and introducing the desired trajectory dynamics, an optimal tracking problem is established. An adaptive dynamic programming (ADP) scheme is employed to obtain the nearly optimal perimeter control law by approximating the solution of the corresponding Hamilton-Jacobi-Bellman (HJB) equation. Furthermore, the proposed scheme guarantees that the tracking error in the closed-loop system is uniformly ultimately bounded. Finally, a two-region network is utilized to demonstrate the effectiveness of the proposed method.